High Dimensional Molecular Data (HDMD) typically have many
more variables or dimensions than observations or replicates
(D>>N).  This can cause many statistical procedures to fail,
become intractable, or produce misleading results.  This
package provides several tools to reduce dimensionality and
analyze biological data for meaningful interpretation of
results. Factor Analysis (FA), Principal Components Analysis
(PCA) and Discriminant Analysis (DA) are frequently used
multivariate techniques.  However, PCA methods prcomp and
princomp do not reflect the proportion of total variation of
each principal component.  Loadings.variation displays the
relative and cumulative contribution of variation for each
component by accounting for all variability in data. When D>>N,
the maximum likelihood method cannot be applied in FA and the
the principal axes method must be used instead, as in factor.pa
of the psych package. The factor.pa.ginv function in this
package further allows for a singular covariance matrix by
applying a general inverse method to estimate factor scores.
Moreover, factor.pa.ginv removes and warns of any variables
that are constant, which would otherwise create an invalid
covariance matrix. Promax.only further allows users to define
rotation parameters during factor estimation.  Similar to the
Euclidean distance, the Mahalanobis distance estimates the
relationship among groups.  pairwise.mahalanobis computes all
such pairwise Mahalanobis distances among groups and is useful
for quantifying the separation of groups in DA. Genetic
sequences are composed of discrete alphabetic characters, which
makes estimates of variability difficult.  MolecularEntropy and
MolecularMI calculate the entropy and mutual information to
estimate variability and covariability, respectively, of DNA or
Amino Acid sequences.  Functional grouping of amino acids
(Atchley et al 1999) is also available for entropy and mutual
information estimation.  Mutual information values can be
normalized by NMI to account for the background distribution
arising from the stochastic pairing of independent, random
sites. Alternatively, discrete alphabetic sequences can be
transformed into biologically informative metrics to be used in
various multivariate procedures.  FactorTransform converts
amino acid sequences using the amino acid indices determined by
Atchley et al 2005.